So to use the elimination method, we need to put these equations on top of each other so that we can eliminate a variable:
[tex] 2x+4y=8 [/tex]
[tex] 6x+10y=30 [/tex]
If we multiply the top equation by -3, we can eliminate the x variable:
[tex] -3(2x+4y=8) [/tex]
[tex] 6x+10y=30 [/tex]
And we simplify. Then we add the two equations together:
[tex] -6x-12y=-24 [/tex]
+ [tex] 6x+10y=30 [/tex]
---------------------------------
[tex] -2y=6 [/tex]
Then we solve for y:
[tex] y=-3 [/tex]
Then we need to return to one of the original equations (either will work) and plug y in. Then we will solve for x. Let's choose the first equation:
[tex] 2x+4y=8 [/tex]
[tex] 2x+4(-3)=8 [/tex]
[tex] 2x-12=8 [/tex]
[tex] 2x=20 [/tex]
[tex] x=10 [/tex]
So now we know that our solution is: (10, -3).
